Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.5, Problem 2.51P
To determine
Potential on rim of uniformly charged disk.
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4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in
free space. (a) Find the total charge for each distribution. (b) Find the
potential at P(0, 0, 6) caused by each of the three charge distributions
acting alone. (c) Find Vp.
%3D
(0, 5, 0)|
PLA=A nC/m
20°
z=0 plane
(0, 3, 0)
p= 3
PLB= 1.5 nC/m
10°
10°
p=1.6
p= 3.5
Psc 1 nC/m2
20°
FIGURE 4.11
See Prob. 20.
4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in
free space. (a) Find the total charge for each distribution. (b) Find the
potential at P(0, 0, 6) caused by each of the three charge distributions
acting alone. (c) Find Vp.
(0, 5, 0)
P-I nC/m
20°
z-0 plane
(0, 3, 0)
p-3
Pu=1.5 nC/m
10°
p-1.6
10°
p-3.5
PacI nCim?
20
FIGURE 4.1I
A sphere of radius R, centered at the origin, carries charge densityρ(r, θ) = kRr^2(R − 2r ) cos θwhere k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere.
Chapter 2 Solutions
Introduction to Electrodynamics
Ch. 2.1 - (a) Twelve equal charges,q, arc situated at the...Ch. 2.1 - Find the electric field (magnitude and direction)...Ch. 2.1 - Find the electric field a distance z above one end...Ch. 2.1 - Prob. 2.4PCh. 2.1 - Prob. 2.5PCh. 2.1 - Find the electric field a distance z above the...Ch. 2.1 - Find the electric field a distance z from the...Ch. 2.2 - Use your result in Prob. 2.7 to find the field...Ch. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10P
Ch. 2.2 - Use Gauss’s law to find the electric field inside...Ch. 2.2 - Prob. 2.12PCh. 2.2 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - A thick spherical shell carries charge density...Ch. 2.2 - A long coaxial cable (Fig. 2.26) carries a uniform...Ch. 2.2 - Prob. 2.17PCh. 2.2 - Prob. 2.18PCh. 2.2 - Prob. 2.19PCh. 2.3 - One of these is an impossible electrostatic field....Ch. 2.3 - Prob. 2.21PCh. 2.3 - Find the potential a distance s from an infinitely...Ch. 2.3 - Prob. 2.23PCh. 2.3 - Prob. 2.24PCh. 2.3 - Prob. 2.25PCh. 2.3 - Prob. 2.26PCh. 2.3 - Prob. 2.27PCh. 2.3 - Prob. 2.28PCh. 2.3 - Prob. 2.29PCh. 2.3 - Prob. 2.30PCh. 2.4 - Prob. 2.31PCh. 2.4 - Prob. 2.32PCh. 2.4 - Prob. 2.33PCh. 2.4 - Find the energy stored in a uniformly charged...Ch. 2.4 - Prob. 2.35PCh. 2.4 - Prob. 2.36PCh. 2.4 - Prob. 2.37PCh. 2.5 - A metal sphere of radius R, carrying charge q, is...Ch. 2.5 - Prob. 2.39PCh. 2.5 - Prob. 2.40PCh. 2.5 - Prob. 2.41PCh. 2.5 - Prob. 2.42PCh. 2.5 - Prob. 2.43PCh. 2.5 - Prob. 2.44PCh. 2.5 - Prob. 2.45PCh. 2.5 - If the electric field in some region is given (in...Ch. 2.5 - Prob. 2.47PCh. 2.5 - Prob. 2.48PCh. 2.5 - Prob. 2.49PCh. 2.5 - Prob. 2.50PCh. 2.5 - Prob. 2.51PCh. 2.5 - Prob. 2.52PCh. 2.5 - Prob. 2.53PCh. 2.5 - Prob. 2.54PCh. 2.5 - Prob. 2.55PCh. 2.5 - Prob. 2.56PCh. 2.5 - Prob. 2.57PCh. 2.5 - Prob. 2.58PCh. 2.5 - Prob. 2.59PCh. 2.5 - Prob. 2.60PCh. 2.5 - Prob. 2.61P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- A thin conducting disk of radius R, in a vacuum space, is placed on the a – y plane, and is held at a potential Vo. Find the electrostatic potential V (7) (that is the solution of the Laplace equation V'V = 0 under suitable BC) everywhere in space. Find also the areal charge density o on the disk.arrow_forwardfunction. 2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: Ao A(z) = { db e exp(-2/a) z≥0 x 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming Þ(r → ∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.arrow_forward4.20 Fig. 4.11 shows three separate charge distributions in the z = 0 plane in free space. (a) Find the total charge for each distribution. (b) Find the potential at P(0, 0, 6) caused by each of the three charge distributions acting alone. (c) Find Vp. (0, 5, 0) PLA=A nC/m 20° z=0 plane (0, 3, 0) p=3 PLB=1.5 nC/m 10° 10° p= 1.6 p=3.5 Psc=1 nC/m² 20° FIGURE 4.11 See Prob. 20.arrow_forward
- A sphere of radius R centered at the origin carries charge density ρ(r, θ) = k*(R/r^ 2) (R − 2r) sin θ where k is a constant, and r, θ are the usual spherical coordinates. Use the multipole expansion to find the approximate potential for points on the z-axis far from the sphere (z >> R).arrow_forwardThe general solution for the potential (spherical coordinates with azimuthal symmetry) is: +∞ ΣAir² + P₁(Cos 0) B₁ pl+1 l=0 V(r, 0) = Consider a specific charge density (0) = k cos³0, where k is constant, that is glued over the surface of a spherical shell of radius R. Solve for the potential inside the sphere. Hint: Express the surface charge density as a linear combination of the Legendre polynomials.arrow_forward[ Q.3 A capacitor has orthogonal plates of length a and width b. The distance between the plates is h<< a, b. The capacitor has a charge Q. The space between the plates is initially vacuum and we insert slowly a slab of dielectric material as of dielectric constant & as shown in figure. What is the force that is exerted on the slab when it has entered a distance x inside the capacitor? aarrow_forward
- Find the potential on the z axis (0,0,h) produced by an annular(s) ring of uniform surface charge density p, in free space. The ring occupies the region z= 0, p≤a, 0≤ ≤27 in cylindrical coordinates.arrow_forwardLAPLACE In spherical coordinates with azimuthal symmetry, the general solution for the potential is given by +∞ V(r,0) = Air¹ +P₁(cos) Σ A₁r¹ l=0 Consider a specific charge density (0) = k cos³0, where k is constant, that is glued over the surface of a spherical shell of radius R. a. Solve for the potential inside the sphere. [15] Hint: Express the surface charge density as a linear combination of the Legendre polynomials.arrow_forward3. Given the following scalar potentials (V), calculate the solution for the gradient of V (VV), and plot the vector arrow representation of this vector field over the given limits. (a) V = 15 + r cos o, for 0 < r < 10, and 0 < $ < 2n. (b) V = 100 + xy, for –10 < x < 10,arrow_forward
- Lets say there is a spherical thin shell of radius a. It carries uniform surface chargewith a density of ps C/m2, (p is ro). I want to find the potential V for points outside the spherical shell and inside the shell. (The reference point for V is set at infinity.) Plot V as a function of R. Thank you for helping me with this practice.arrow_forwardFind the Electric flux density D in the free space at point (2,0, n/2), if the potential V =- sin 0 sin Ø?.arrow_forwardBy using the general solution with cylindrical symmetry V(s,4) = ao + bo In s+[*(@+ cos ko + be sin kø) + s¯*(c& cos kø + dg sin kø)]. Find the potential outside an infinitely long metal pipe, of radius R placed at right angles to an otherwise uniform electric field Eo. Find the surface charge induced on the pipe.arrow_forward
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